Question

# 1. (3 points) Little recap from Math 1148. Graph transformations of a function correspond to changes in the formula of that same function. For example, taking the graph of g(x) = x² and shifting it up by 2 units changes the formula of g(x) = r² to g1(x) = g(x) + 2 = x² + 2. If I now take the graph of 91 (x) = r² + 2 and apply a vertical stretch by a factor of 3, the formula of g1(x) = x² + 2 changes to 92(r) = 3 g1(x) = 3(x² + 2) = 3x² + 6. Conversely, if I am given the function k(x) = 3(r – 2)² – 1, I can list the graph transformations, in order, that turn the graph of h(x) = x² into the graph of k(x).First, I take the graph of h(x) = a² and shift it to the right by 2 units (this changes h(x) = x² to h1(r) = h(x – 2) = (r – 2)²); then, I apply to the resulting graph a vertical stretch by a factor of 3 (this changes h (x) = (r – 2)² to h2(x) = 3(r – 2)²); finally, I apply to the resulting graph a shift down by 1 unit (this changes h2(x) = 3(x – 2)² to h3(x) = h2(x) –1 = 3(x – 2)² – 1 = k(x)). Note that I need to first stretch vertically and then shift down: reversing the order of these operations produces the formula for a function different from k(r). Now, to your exercise. List all the graph transformations, in order, that turn the graph of g(x) = cos(r)into the graph of f(x) = -2 cos(x + 3) – 4.  Fig: 1  Fig: 2  Fig: 3